HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation

Estimating the Jacobian of the Singular Value Decomposition : Theory and Applications

Théodore Papadopoulo 1 Manolis L.A. Lourakis 1
1 ROBOTVIS - Computer Vision and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The Singular Value Decomposition (SVD) of a matrix is a linear algebra tool that has been successfully applied to a wide variety of domains. The present paper is concerned with the problem of estimating the Jacobian of the SVD components of a matrix with respect to the matrix itself. An exact analytic technique is developed that facilitates the estimation of the Jacobian using calculations based on simple linear algebra. Knowledge of the Jacobian of the SVD is very useful in certain applications involving multivariate regression or the computation of the uncertainty related to estimates obtained through the SVD. The usefulness and generality of the proposed technique is demonstrated by applying it to the estimation of the uncertainty for three different vision problems, namely self-calibratio- n, epipole computation and rigid motion estimation.
Document type :
Complete list of metadata

Cited literature [46 references]  Display  Hide  Download

Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Wednesday, May 24, 2006 - 10:35:30 AM
Last modification on : Friday, February 4, 2022 - 3:15:36 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:18:34 PM


  • HAL Id : inria-00072686, version 1



Théodore Papadopoulo, Manolis L.A. Lourakis. Estimating the Jacobian of the Singular Value Decomposition : Theory and Applications. [Research Report] RR-3961, INRIA. 2000, pp.21. ⟨inria-00072686⟩



Record views


Files downloads